Next generation giant telescopes are under study around the world, with great variety in size and pupil segmentation scheme. We present performance calculations for different pupil segmentation geometries for 20 - 30 m class telescopes. Parameters include segment size and shape, gap diffraction, and segment surface errors. Optical performance is evaluated through point-spread function (PSF) calculation for the different concepts. Segments are large, 8m-class, circular or polygonal mirrors, or small, 2m-class, hexagonal mirrors. These options represent the choices of the different communities involved in the studies for the Next Generation Canada-France-Hawaii Telescope. Our segmentation scheme consists of eight 8m-class polygonal petals forming a filled octagonal 20 m pupil. All segment and pupil edges are along four unique directions, minimizing the number of diffraction arms in the PSF, and creating large areas of low levels of scattered light close to the core. This is important for high-dynamic range imaging. Comparison between polygonal and circular petals shows that, in addition to the presence of low-scatter areas, the encircled energy is higher. Impact on optical performance of atmospheric perturbations and residual wavefront errors after correction by an Adaptive Optics system are also discussed.